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The Class Number of the Cyclotomic Field. [PDF]
Proc Natl Acad Sci U S A, 1949 Let g denote an odd prime, and h = h(g) the class number of the cyclotomic field R(), where is a primitive gth root of unity. It is known that we can write
Ankeny NC, Chowla S.
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The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings [PDF]
Entropy, 2021 Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring ...
Jheyne N. Ortiz +4 more
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Research on Linear Complexity of Quaternary Sequences with Period 2pq [PDF]
Jisuanji gongcheng, 2016 Linear complexity is an important index for measuring the randomness properties of the sequences.Based on the theory of generalized cyclotomic,a new class of quaternary balanced generalized cyclotomic sequences with period 2pq over finite field F4 is ...
WEI Wanyin,DU Xiaoni,WANG Guohui
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On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12
Recoletos Multidisciplinary Research Journal, 2023 Almost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime ...
Benedict Estrella
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The linear complexity of new q-ary generalized cyclotomic sequences of period pn [PDF]
MATEC Web of Conferences, 2019 In this paper, we study the linear complexity of new q-ary generalized cyclotomic sequences of length pn over the finite field of order q. We show that these sequences have the high linear complexity when n ≥ 2.
Edemskiy Vladimir, Sokolovskiy Nikita
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Construction of Difference Sets from Unions of Cyclotomic Classes of Order N=14
Recoletos Multidisciplinary Research Journal, 2022 Let G be an additive group of order v, D be a non-empty proper k-subset of G, and λ be any integer. Then D is a (v, k, λ) - difference set if every nonzero element of the group can be expressed as a difference d1 - d2 of elements of D in exactly
Benedict Estrella
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Construction of quantum BCH code based on cyclotomic coset
Tongxin xuebao, 2021 Quantum-error-correcting code can overcome quantum decoherence efficiently, which is the key technology to realize quantum computers.A series of quantum BCH code was proposed based on classical codes.First, a general way of well-chosen cyclotomic coset ...
Lijuan XING, Zhuo LI
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On cyclotomic elements and cyclotomic subgroups in $K_{2}$ of a field [PDF]
Acta Arithmetica, 2016 The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit form. In this paper, we modify and change Browkin's conjecture about cyclotomic elements into more precise forms, in
Xu, Kejian, Sun, Chaochao
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Cyclotomic splitting fields [PDF]
Proceedings of the American Mathematical Society, 1970 Suppose k is an algebraic nunmber field and D a finite- dimensional central division algebra over k. It is well known that D has infinitely many maximal subfields which are cyclic exten- sions of k. From the point of view of group representations, how- ever, the natural splitting fields are the cyclotomnic ones.
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ON WEIL NUMBERS IN CYCLOTOMIC FIELDS [PDF]
International Journal of Number Theory, 2009 In this paper, we study the p-adic behavior of Weil numbers in the cyclotomic ℤp-extension of the pth cyclotomic field. We determine the characteristic ideal of the quotient of semi-local units by Weil numbers in terms of the characteristic ideals of some classical modules that appear in the Iwasawa theory.
Anglès, Bruno, Beliaeva, Tatiana
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